Pub Date : 2023-07-31DOI: 10.1177/03093247231190449
Mohammad A. Gharaibeh, J. Wilde
This paper aims to examine the thermomechanical response of sintered silver die attachments in power electronics using finite element analysis (FEA). In this work, several material parameters of the sintered silver bonds are investigated. Additionally, two common solder creep constitutive laws including Anand and Garofalo models are also studied. To ensure the fidelity of the simulation procedures, the finite element (FE) models are first correlated with digital image correlation data. Afterward, the FE models are utilized to examine the influence of the material and creep models on the die attach stresses, strains, and plastic works. The expected fatigue and lifetime predictions of the sintered silver layer are thoroughly discussed, accordingly. The results proved that the die attach layer mechanical response is highly driven by the material parameters and creep modeling procedures considered throughout the simulations. Thus, the resulting fatigue life is evaluated. Finally, a general modeling guideline for simulating thermomechanical response of sintered silver die attachments in power electronics are provided in great detail.
{"title":"Applying Anand versus Garofalo creep constitutive models for simulating sintered silver die attachments in power electronics","authors":"Mohammad A. Gharaibeh, J. Wilde","doi":"10.1177/03093247231190449","DOIUrl":"https://doi.org/10.1177/03093247231190449","url":null,"abstract":"This paper aims to examine the thermomechanical response of sintered silver die attachments in power electronics using finite element analysis (FEA). In this work, several material parameters of the sintered silver bonds are investigated. Additionally, two common solder creep constitutive laws including Anand and Garofalo models are also studied. To ensure the fidelity of the simulation procedures, the finite element (FE) models are first correlated with digital image correlation data. Afterward, the FE models are utilized to examine the influence of the material and creep models on the die attach stresses, strains, and plastic works. The expected fatigue and lifetime predictions of the sintered silver layer are thoroughly discussed, accordingly. The results proved that the die attach layer mechanical response is highly driven by the material parameters and creep modeling procedures considered throughout the simulations. Thus, the resulting fatigue life is evaluated. Finally, a general modeling guideline for simulating thermomechanical response of sintered silver die attachments in power electronics are provided in great detail.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81096746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-27DOI: 10.1177/03093247231188762
A. M. Abd-Alla, D. M. Salah
The purpose of the current study is to establish the deformation in a two-dimensional, isotropic, rotating half-space with gravitational field and initial stress that also has a heat source at the half boundary-space under magnetic field for Green and Naghdi II model. For the solution of the required problem, the methodologies of normal mode and approximate eigenvalues has been utilized. For graphical representation of different physical quantities such as displacement components, stress components, as well as the temperature distribution, Matlab software has been used. These results were compared with previous results in the same direction, and it was found that the treatment method for the aforementioned problem may form a basis for examining the effect of each of the gravitational field, magnetic field, rotation, and initial pressure on a thermally elastic body in the form of half an area without energy decay when neglecting some external influences.
{"title":"Effect of initial stress and rotation on magneto-thermoelastic half-space with gravity field and without energy dissipation","authors":"A. M. Abd-Alla, D. M. Salah","doi":"10.1177/03093247231188762","DOIUrl":"https://doi.org/10.1177/03093247231188762","url":null,"abstract":"The purpose of the current study is to establish the deformation in a two-dimensional, isotropic, rotating half-space with gravitational field and initial stress that also has a heat source at the half boundary-space under magnetic field for Green and Naghdi II model. For the solution of the required problem, the methodologies of normal mode and approximate eigenvalues has been utilized. For graphical representation of different physical quantities such as displacement components, stress components, as well as the temperature distribution, Matlab software has been used. These results were compared with previous results in the same direction, and it was found that the treatment method for the aforementioned problem may form a basis for examining the effect of each of the gravitational field, magnetic field, rotation, and initial pressure on a thermally elastic body in the form of half an area without energy decay when neglecting some external influences.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81506900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.1177/03093247231187015
Rui F. V. Sampaio, João P. M. Pragana, I. Bragança, Carlos MA Silva, Paulo A. F. Martins
This paper presents an upset geometry sequence to determine the fracture forming limits in a wide variety of strain loading paths ranging from uniaxial compression to equibiaxial tension. The strains at fracture in principal strain space are obtained by combination of digital image correlation and experimental evolutions of the compression force versus time, and their representation in the effective strain versus stress triaxiality space is accomplished by means of a new analytical framework that uses the instantaneous slope of the strain loading paths. Modeling of the experimental strains at fracture by means of an uncoupled ductile fracture criterion built upon combination of the Cockcroft-Latham and McClintock criteria and fractography analysis using a scanning electron microscope allow understanding and characterizing the crack opening modes by shear and tension as well as the uncertainty region inside which mixed crack opening modes are observed. Results confirm that the overall philosophy and objectives underlying the new upset geometry sequence for determining the fracture forming limits in bulk forming resemble those of the Nakajima test that is commonly used in sheet forming.
{"title":"A complete characterization of THE fracture forming limits in bulk forming by means of an upset geometry sequence","authors":"Rui F. V. Sampaio, João P. M. Pragana, I. Bragança, Carlos MA Silva, Paulo A. F. Martins","doi":"10.1177/03093247231187015","DOIUrl":"https://doi.org/10.1177/03093247231187015","url":null,"abstract":"This paper presents an upset geometry sequence to determine the fracture forming limits in a wide variety of strain loading paths ranging from uniaxial compression to equibiaxial tension. The strains at fracture in principal strain space are obtained by combination of digital image correlation and experimental evolutions of the compression force versus time, and their representation in the effective strain versus stress triaxiality space is accomplished by means of a new analytical framework that uses the instantaneous slope of the strain loading paths. Modeling of the experimental strains at fracture by means of an uncoupled ductile fracture criterion built upon combination of the Cockcroft-Latham and McClintock criteria and fractography analysis using a scanning electron microscope allow understanding and characterizing the crack opening modes by shear and tension as well as the uncertainty region inside which mixed crack opening modes are observed. Results confirm that the overall philosophy and objectives underlying the new upset geometry sequence for determining the fracture forming limits in bulk forming resemble those of the Nakajima test that is commonly used in sheet forming.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72413053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1177/03093247231179006
K. Ganesan, Saravanan Sambasivam, R. Ramadass
The deep drawing technique is an important metal forming processes, and it is rarely used in the Inconel 718 sheet. The main purpose of this study is to perform a deep drawing process using the Inconel 718 alloy. In this research article, the Inconel 718 alloy sheet of 1 mm thickness is drawn into sheet metal cups, and defects such as thinning, and earing are controlled using selected input parameters such as Blank Holding Force (BHF) Blank Diameter (BD), and Punch Nose Radius (Rpn). A Box Behnken design (BBD) is used to evaluate the effects of output parameters. The hybrid Deep Neural Network (DNN) is used to predict the experimental outcomes obtained from the deep drawing process. For deep drawing process blank holding force is favorable for both thinning and earing. The minimum thinning value obtained during experimentation is 0.033 mm. During experimentation less earing value is 2.47 mm. Hybrid Deep Neural Network based Sparrow Search Optimization (DNN-SSO) gives the prediction model, where the values are much closer to the experimented model than RSM and non-Hybrid DNN. The minimum thinning obtained in the prediction model such as RSM, SSO-DNN, and DNN are 0.030, 0.0304, and 0.023 mm. Likewise, the minimum earing obtained from the predictive model is 2.65, 2.49, and 2.51 mm respectively. The minimum error is found in the hybrid DNN and the average RMSE for thinning is 0.002 and earing is 0.0024. The regression coefficient of thinning and earing is 99% which proves the experimental outcomes matches with RSM validation.
{"title":"Predicting and improving the novel process parameters involved in deep drawing process of Inconel 718 sheet at room temperature using hybrid DNN-SSO approach","authors":"K. Ganesan, Saravanan Sambasivam, R. Ramadass","doi":"10.1177/03093247231179006","DOIUrl":"https://doi.org/10.1177/03093247231179006","url":null,"abstract":"The deep drawing technique is an important metal forming processes, and it is rarely used in the Inconel 718 sheet. The main purpose of this study is to perform a deep drawing process using the Inconel 718 alloy. In this research article, the Inconel 718 alloy sheet of 1 mm thickness is drawn into sheet metal cups, and defects such as thinning, and earing are controlled using selected input parameters such as Blank Holding Force (BHF) Blank Diameter (BD), and Punch Nose Radius (Rpn). A Box Behnken design (BBD) is used to evaluate the effects of output parameters. The hybrid Deep Neural Network (DNN) is used to predict the experimental outcomes obtained from the deep drawing process. For deep drawing process blank holding force is favorable for both thinning and earing. The minimum thinning value obtained during experimentation is 0.033 mm. During experimentation less earing value is 2.47 mm. Hybrid Deep Neural Network based Sparrow Search Optimization (DNN-SSO) gives the prediction model, where the values are much closer to the experimented model than RSM and non-Hybrid DNN. The minimum thinning obtained in the prediction model such as RSM, SSO-DNN, and DNN are 0.030, 0.0304, and 0.023 mm. Likewise, the minimum earing obtained from the predictive model is 2.65, 2.49, and 2.51 mm respectively. The minimum error is found in the hybrid DNN and the average RMSE for thinning is 0.002 and earing is 0.0024. The regression coefficient of thinning and earing is 99% which proves the experimental outcomes matches with RSM validation.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74576088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-13DOI: 10.1177/03093247231173741
H. Saeed, Somsubhro Chaudhuri, W. De Waele
Short fatigue crack growth investigation is of considerable scientific interest as it comprises a significant portion of the total fatigue life of a structure. It is very challenging to accurately quantify this stage of fatigue crack growth experimentally. In this article, a novel front face strain compliance technique for single-edge notched specimens subjected to four-point bending is proposed. Finite element analysis is performed to determine the correlation between crack length and strain change near the crack. This relationship is then validated by experiments in which strains are measured by strain gauges attached near the short crack, and crack length is quantified by examining beachmark lines at the fracture surfaces. Based on the numerical and experimental results, it is concluded that the strain measured near the notch allows quantifying short crack growth for normalised crack lengths in the range 0.01 ≤ a/W ≤ 0.06 (a/W being the ratio of crack length over specimen width). A compliance equation based on the front face strain is finally presented.
{"title":"Front face strain compliance for quantification of short crack growth in fatigue testing","authors":"H. Saeed, Somsubhro Chaudhuri, W. De Waele","doi":"10.1177/03093247231173741","DOIUrl":"https://doi.org/10.1177/03093247231173741","url":null,"abstract":"Short fatigue crack growth investigation is of considerable scientific interest as it comprises a significant portion of the total fatigue life of a structure. It is very challenging to accurately quantify this stage of fatigue crack growth experimentally. In this article, a novel front face strain compliance technique for single-edge notched specimens subjected to four-point bending is proposed. Finite element analysis is performed to determine the correlation between crack length and strain change near the crack. This relationship is then validated by experiments in which strains are measured by strain gauges attached near the short crack, and crack length is quantified by examining beachmark lines at the fracture surfaces. Based on the numerical and experimental results, it is concluded that the strain measured near the notch allows quantifying short crack growth for normalised crack lengths in the range 0.01 ≤ a/W ≤ 0.06 (a/W being the ratio of crack length over specimen width). A compliance equation based on the front face strain is finally presented.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79805206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-19DOI: 10.1177/03093247231164261
B. Uzun, M. Yaylı
A novel stability model is analytically reformulated for the nano-sized beam resting on a one-parameter elastic foundation. The stability solution is based on the nonlocal strain gradient elasticity theory. To corporate the small size effects, two small scale parameters are introduced. The six-order ordinary differential form of the buckling equation, together with two force boundary conditions, are utilized to examine the stability equation in terms of lateral deflection. The infinite terms of linear equations are discretized with the help of the Stokes’ transformation and Fourier sine series. The present work can investigate the effects of elastic spring parameters at the ends, nonlocal properties, elastic medium properties, strain gradient parameter, and buckling behavior of the nanobeam. The predictions of the proposed analytical model with deformable boundary conditions are in agreement with those available in the scientific literature for the nanobeam on elastic foundation based on a closed form of solution. The presence of the deformable conditions, elastic foundation, nonlocal, and strain gradient properties change the buckling loads and buckling mode shapes.
{"title":"Stability analysis of arbitrary restrained nanobeam embedded in an elastic medium via nonlocal strain gradient theory","authors":"B. Uzun, M. Yaylı","doi":"10.1177/03093247231164261","DOIUrl":"https://doi.org/10.1177/03093247231164261","url":null,"abstract":"A novel stability model is analytically reformulated for the nano-sized beam resting on a one-parameter elastic foundation. The stability solution is based on the nonlocal strain gradient elasticity theory. To corporate the small size effects, two small scale parameters are introduced. The six-order ordinary differential form of the buckling equation, together with two force boundary conditions, are utilized to examine the stability equation in terms of lateral deflection. The infinite terms of linear equations are discretized with the help of the Stokes’ transformation and Fourier sine series. The present work can investigate the effects of elastic spring parameters at the ends, nonlocal properties, elastic medium properties, strain gradient parameter, and buckling behavior of the nanobeam. The predictions of the proposed analytical model with deformable boundary conditions are in agreement with those available in the scientific literature for the nanobeam on elastic foundation based on a closed form of solution. The presence of the deformable conditions, elastic foundation, nonlocal, and strain gradient properties change the buckling loads and buckling mode shapes.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80007171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-31DOI: 10.1177/03093247231165091
A. Eldeeb, Y. Shabana, A. Elsawaf
In this paper, the particle swarm optimization method is used to reduce the weight of a multilayer rotating nonuniform thickness disc along with alleviation of the maximum tangential stress and the maximum tangential stress-jump at the interfaces. The proposed disc is made of functionally graded material and is subjected to both mechanical pressure and thermal loads. It is divided into several layers with each one having its unique volume fraction. These volume fractions are considered the design variables of the optimization problem along with two geometrical parameters related to the disc thickness. The equilibrium equation in polar coordinates are solved using the finite difference method. A punch of optimization results is calculated and discussed. It is concluded that the range of design variables’ variation widens by considering more layers. Finally, there is no potential disc configuration or geometry is found dominant to enhance the design parameters concurrently. Therefore, performing similar optimization analyses is compulsory to obtain an efficient and durable structure.
{"title":"Thermoelastic stress mitigation and weight reduction of functionally graded multilayer nonuniform thickness disc","authors":"A. Eldeeb, Y. Shabana, A. Elsawaf","doi":"10.1177/03093247231165091","DOIUrl":"https://doi.org/10.1177/03093247231165091","url":null,"abstract":"In this paper, the particle swarm optimization method is used to reduce the weight of a multilayer rotating nonuniform thickness disc along with alleviation of the maximum tangential stress and the maximum tangential stress-jump at the interfaces. The proposed disc is made of functionally graded material and is subjected to both mechanical pressure and thermal loads. It is divided into several layers with each one having its unique volume fraction. These volume fractions are considered the design variables of the optimization problem along with two geometrical parameters related to the disc thickness. The equilibrium equation in polar coordinates are solved using the finite difference method. A punch of optimization results is calculated and discussed. It is concluded that the range of design variables’ variation widens by considering more layers. Finally, there is no potential disc configuration or geometry is found dominant to enhance the design parameters concurrently. Therefore, performing similar optimization analyses is compulsory to obtain an efficient and durable structure.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90847217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-31DOI: 10.1177/03093247231166035
B. Zettl, H. Schmid, S. Pulvermacher, Alexander Dyck, T. Böhlke, J. Gibmeier, M. Merklein
In scientific studies, sheet metal is usually considered as a two-dimensional body. Thus, it is accepted that material properties are in most cases regarded homogeneous in thickness direction. However, a gradation of certain properties becomes apparent when going beyond the standard characterization methods for sheet metals, which can for example, influence the springback behavior and the thinning of the sheet after forming. Thus, the aim of this work is to further improve the prediction accuracy of springback after forming in simulations, by implementing several inhomogeneous properties over the sheet thickness in an existing material model. For this purpose, the entire procedure from the identification of the inhomogeneous properties for describing the gradation to the implementation in a numerical model and its validation by comparing experimental and simulated bending operations is carried out on a DC04 cold-forming steel in order to prove its influence on the springback behavior. It is shown that including graded material properties in simulations does indeed have an impact on the prediction quality of springback and that the information about inhomogeneous properties can be provided by existing characterization methods with a high local resolution like electron backscatter diffraction or X-ray stress analysis. In a further step, it was possible to validate the improvement in numerical accuracy by comparing the prediction of the springback angle from both the existing and the extended model with experimental bending results. Both the initial model as well as the model supplemented with the 3D properties provide a good prediction accuracy in the solution heat treated material state. For the predeformed material, however, the initial numerical model predicts a springback angle of about 13°, which deviates remarkably from the experimentally obtained mean value of about 17°. The extended model delivers a significantly improved accuracy in springback prediction in relation to the initial prediction (deviation of 4°) with a minor deviation of only about 0.8°, which proves the importance of considering the gradation of material properties in thickness direction for an overall higher dimensional accuracy of sheet metal products.
{"title":"Improvement of process control in sheet metal forming by considering the gradual properties of the initial sheet metal","authors":"B. Zettl, H. Schmid, S. Pulvermacher, Alexander Dyck, T. Böhlke, J. Gibmeier, M. Merklein","doi":"10.1177/03093247231166035","DOIUrl":"https://doi.org/10.1177/03093247231166035","url":null,"abstract":"In scientific studies, sheet metal is usually considered as a two-dimensional body. Thus, it is accepted that material properties are in most cases regarded homogeneous in thickness direction. However, a gradation of certain properties becomes apparent when going beyond the standard characterization methods for sheet metals, which can for example, influence the springback behavior and the thinning of the sheet after forming. Thus, the aim of this work is to further improve the prediction accuracy of springback after forming in simulations, by implementing several inhomogeneous properties over the sheet thickness in an existing material model. For this purpose, the entire procedure from the identification of the inhomogeneous properties for describing the gradation to the implementation in a numerical model and its validation by comparing experimental and simulated bending operations is carried out on a DC04 cold-forming steel in order to prove its influence on the springback behavior. It is shown that including graded material properties in simulations does indeed have an impact on the prediction quality of springback and that the information about inhomogeneous properties can be provided by existing characterization methods with a high local resolution like electron backscatter diffraction or X-ray stress analysis. In a further step, it was possible to validate the improvement in numerical accuracy by comparing the prediction of the springback angle from both the existing and the extended model with experimental bending results. Both the initial model as well as the model supplemented with the 3D properties provide a good prediction accuracy in the solution heat treated material state. For the predeformed material, however, the initial numerical model predicts a springback angle of about 13°, which deviates remarkably from the experimentally obtained mean value of about 17°. The extended model delivers a significantly improved accuracy in springback prediction in relation to the initial prediction (deviation of 4°) with a minor deviation of only about 0.8°, which proves the importance of considering the gradation of material properties in thickness direction for an overall higher dimensional accuracy of sheet metal products.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87795405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-27DOI: 10.1177/03093247231163205
Yifeng Chen, D. Hills
The shakedown limit for an infinite plate containing a circular hole and subject to oscillatory arbitrary remote loading is found, first by using Melan’s lower bound theorem, and secondly by using a finite element model. It is shown that in some cases the limit found from the Melan theorem using the solution for the residual state of stress for an over-pressurized hole provides the exact solution, specifically when the limiting factor is the reversal of the state of stress at a particular point, while in other cases the shakedown limit is rather higher.
{"title":"Shakedown of a plate with a circular hole: An educational problem","authors":"Yifeng Chen, D. Hills","doi":"10.1177/03093247231163205","DOIUrl":"https://doi.org/10.1177/03093247231163205","url":null,"abstract":"The shakedown limit for an infinite plate containing a circular hole and subject to oscillatory arbitrary remote loading is found, first by using Melan’s lower bound theorem, and secondly by using a finite element model. It is shown that in some cases the limit found from the Melan theorem using the solution for the residual state of stress for an over-pressurized hole provides the exact solution, specifically when the limiting factor is the reversal of the state of stress at a particular point, while in other cases the shakedown limit is rather higher.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89306508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-21DOI: 10.1177/03093247231160617
S. Pal, D. Das
The present work studies the free vibration response of functionally graded rotating micro-disks subjected to transverse pressure and thermal loading based on the modified couple stress theory. The disk material is considered to be functionally graded along the radial and thickness directions, and its properties are assumed to be temperature-dependent following the Touloukian model. The mathematical formulation is based on an energy functional involving the von Kármán type non-linearity, in which appropriate displacement derivatives and its conjugate stress measures are used to define the strain energy of the micro-disk. The minimum potential energy principle is employed to develop the governing equations for determining the deformed configuration of the micro-disk under combined centrifugal, pressure and thermal loading. Further, the governing equations for free vibratory motion of the micro-disk are derived following Hamilton’s principle and incorporating the tangent stiffness of the deformed micro-disk. The governing equations are discretized and solved employing the Ritz method. The mathematical model is successfully validated with different reduced problems available in the literature. The influence of rotational speed, transverse pressure, thermal loading, size-dependent thickness and volume fraction indices are investigated for a wide range of parametric values. Some illustrative mode shapes along with the contour have also been presented. The present study is first of its kind and the presented results would definitely serve as benchmarks for any further study in this field.
{"title":"Free vibration response of bidirectional functionally graded rotating micro-disk under mechanical and thermal loading","authors":"S. Pal, D. Das","doi":"10.1177/03093247231160617","DOIUrl":"https://doi.org/10.1177/03093247231160617","url":null,"abstract":"The present work studies the free vibration response of functionally graded rotating micro-disks subjected to transverse pressure and thermal loading based on the modified couple stress theory. The disk material is considered to be functionally graded along the radial and thickness directions, and its properties are assumed to be temperature-dependent following the Touloukian model. The mathematical formulation is based on an energy functional involving the von Kármán type non-linearity, in which appropriate displacement derivatives and its conjugate stress measures are used to define the strain energy of the micro-disk. The minimum potential energy principle is employed to develop the governing equations for determining the deformed configuration of the micro-disk under combined centrifugal, pressure and thermal loading. Further, the governing equations for free vibratory motion of the micro-disk are derived following Hamilton’s principle and incorporating the tangent stiffness of the deformed micro-disk. The governing equations are discretized and solved employing the Ritz method. The mathematical model is successfully validated with different reduced problems available in the literature. The influence of rotational speed, transverse pressure, thermal loading, size-dependent thickness and volume fraction indices are investigated for a wide range of parametric values. Some illustrative mode shapes along with the contour have also been presented. The present study is first of its kind and the presented results would definitely serve as benchmarks for any further study in this field.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91005765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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